1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nezavi [6.7K]
2 years ago
7

(7 + 7i)(2 − 2i)

Mathematics
1 answer:
Ostrovityanka [42]2 years ago
3 0

The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)

\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)

\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

=21-21i

After converting into the exponential form:

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

You might be interested in
Proportions happen because two events or scenarios are ___
Anni [7]
<span>Proportions happen because two events or scenarios are related or associated with one another </span>
6 0
3 years ago
Hector went shopping for a computer. At RST store, a computer originally prices at $955 had a price reduction of 40%. What was t
balandron [24]

Answer:

$573

Step-by-step explanation:

955* 0.60=573

or

10% of 955= 95.5

50% of 955=477.5

477.5=95.5=573

4 0
3 years ago
6(6v +6) - 5 = 1 + 6v<br><br> Need answer with explaination
Tresset [83]

Answer:

v=-1

Step-by-Step Explanation:

6 0
2 years ago
Read 2 more answers
What is a common factor for the two fractional terms StartFraction 5 over 8 EndFraction x andStartFraction 11 over 8 EndFraction
Dafna1 [17]

Answer:

\frac{1}{8x}

Step-by-step explanation:

Given two fractional terms \frac{5}{8x}\ and\ \frac{11}{8xy}. Their common factor is a value or function that can go in both fractional terms. The terms can be written as shown.

\frac{5}{8x} = 5 *\frac{1}{8x}

\frac{11}{8xy} = 11 * \frac{1}{8x} * \frac{1}{y}

It can be seen from the both equations that they both have \frac{1}{8x} as one of their factors i.e <em>1/8x is common to both fractional terms</em>. This gives the common factor for the two fractional terms as \frac{1}{8x}

4 0
3 years ago
Read 2 more answers
Please someone help me
Vanyuwa [196]
1.
1/4 is less then 2/4 or 1/2so if the denominator is equal it will be easier to multiply
3 0
3 years ago
Other questions:
  • How can you solve problems involving equations that contain addition, subtraction, multiplication, or division
    7·2 answers
  • 5 poin
    14·2 answers
  • Circle with radius 5 inches. round your answer to the nearest tenth
    14·1 answer
  • The radio of boys to girls is 3:4. There were 60 girls at the dance. How many boys were at the dance?
    13·2 answers
  • Fill in the blanks.<br> 2 yd = ?ft<br> 84 in = ?ft
    12·2 answers
  • Write an equation in slope intercept form using the given slope and y-intercept (problem 13)
    14·2 answers
  • 90,100,120,120,140 calculate the median distance
    5·1 answer
  • Find the height of the pyramid.<br> Volume = 224 in.
    13·1 answer
  • Find the probability of rolling a number less<br> than 3 on a die.<br><br><br> Pls help
    10·2 answers
  • Eight decreased by three times the sum of a number and six<br><br> Write as an algebraic expression
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!